# Do I Dare Disturb the Universe? by Madeleine L'Engle

By Madeleine L'Engle

"Do I Dare Disturb the Universe?" is Madeleine L'Engle's lively safety of the accountability of children's literature to confront tricky questions, as she did in all her paintings, rather her masterpiece A Wrinkle in Time. This book includes the textual content of her recognized speech in addition to her creation to the twenty-fifth anniversary of A Wrinkle in Time and a facsimile of a bankruptcy from the unique manuscript with Madeleine's notations.

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**Example text**

Next, we impose concavity of voter utility functions at the outset to prove the utilitarian result. Theorem 6. In the Utility Difference Model, assume (i) X is convex, (ii) for each t and C, Pf{u,v) is strictly monotonic and has partial derivatives with respect to the Cth component bounded in (t^u^v), and (Hi) for each t, ut is concave. If {X%X''Q) is a pure strategy electoral equilibrium, then x\ maximizes (1) and x^ maximizes (2). re positive and independent oft. x\ and x^ maximize (3). Then Assume, moreover, (v) aggregate strict concavity holds.

The next result is closely related to the existence and uniqueness part of Lindbeck and Weibull's [24] Theorem 1, though we strengthen their strict quasi-concavity to strict concavity in order to capture mixed strategy electoral equilibria. We give further uniqueness results in Section 4. Theorem 3. XB), j P^{xA,XB)diJi is strictly concave in XA and f Pf{xA,XB)dfi is strictly concave in XB' Then there is exactly one electoral equilibrium, and it is in pure strategies, Proof, Existence of equilibrium follows from Theorems 1 or 2.

Strict monotonicity, differentiability, or concavity) have a clear interpretation in terms of the primitives of the Additive Bias Model. The Utility Ratio Model. XB) = Pf{Ut{xA)/UtixB))^ An example would be the Multiplicative Bias Model, in which each type t voter draws bias /? and votes for A if Wt(x^) > /3ut{xB)^ votes for B if the inequality is reversed, and flips a coin in the event of equality. When Gt is continuous, expected plurality share functions are again positive affine transformations of bias distributions, and assumptions on the former translate directly to assumptions on the latter.